2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/198899A rigorous (and simple) proof is given that there is a one-to-one correspondence between causal anti-deSitter covariant quantum field theories on anti-deSitter space and causal conformally covariant quantum field theories on its conformal boundary. The correspondence is given by the explicit identification of observables localized in wedge regions in anti-deSitter space and observables localized in double-cone regions in its boundary. It takes vacuum states into vacuum states, and positive-energy representations into positive-energy representations.16 pages, 1 figure, v3: new material added in response to referees' reports, v4: a hasty conclusion in v3 rectified + more cosmetic changesHigh Energy Physics - TheoryGeneral Relativity and Quantum Cosmologytext